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Re: question about series capacitors



I would consider an application of Gauss' Law to the "closed surface"
which bounds A&B (or C&D) together with the knowledge that the total
charge is initially zero on the capacitor pair of plates A&B (or C&D).
This information along with the same reasoning that gave us Qb=Qc requires
that Qa=Qb (and also Qc=Qd). QED


On Wed, 10 Sep 1997, Carl E. Mungan wrote:

Dear PhysLers: I have a question about the usual formula for capacitors in
series, which is different than Ludwik's business about the leakage which
was discussed a few years ago.

Suppose I connect two capacitors in series across a battery. Label the four
capacitor plates from left to right as A, B, C, and D. Okay, suppose A is
connected to the positive terminal of the battery, so out goes charge +Q to
it, and compensating charge off D, leaving -Q on it. My question is: why
does the charge on B and C have to be -Q and +Q, respectively?

If the isolated circuit consisting of plates B and C and the wire between
them is initially uncharged, then the sum of the charges presumably has to
remain zero. But why couldn't I get -1.1Q and +1.1Q on these two plates,
say? Why *exactly* -/+Q? Is it always exact: what if plates A and B have
different shapes? Or what if I imagine distorting the wire between plates B
and C, so that B and C are both portions of some larger object, say the two
ends of a solid rectangular block, or even a sphere? Surely at some point
the answer will no longer be -/+Q. At what point - in other words, what
assumptions go into the usual derivation? I've looked in several textbooks
and it's presented as though -/+Q is patently obvious. Carl

------------------------------------------------------------------------
Dr. Carl Mungan, Assistant Professor http://www.uwf.edu/~cmungan/
Dept. of Physics, University of West Florida, Pensacola, FL 32514-5751
office: 850-474-2645 (secretary -2267, FAX -3131) email: cmungan@uwf.edu




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